



"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable






def 			snake_case_    ( A_   :						Callable[[int | float], int | float],							A_   :						int | float,							A_   :						int | float,							A_   :						int = 1_00,							):


       '''simple docstring'''





       _lowerCamelCase		:							Optional[Any]            =					x_start
       _lowerCamelCase		:							int            =					fnc(A_		)
       _lowerCamelCase		:							Optional[Any]            =					0.0
       for _ in range(A_		):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              _lowerCamelCase		:							int            =					(x_end - x_start) / steps + xa
              _lowerCamelCase		:							Tuple            =					fnc(A_		)
              area += abs(fxa + fxa		) * (xa - xa) / 2
              # Increment step
              _lowerCamelCase		:							Optional[Any]            =					xa
              _lowerCamelCase		:							Any            =					fxa
       return area


if __name__ == "__main__":






   def 			snake_case_    ( A_   :						Optional[int]		):


          '''simple docstring'''





          return x**3 + x**2

   print('''f(x) = x^3 + x^2''')
   print('''The area between the curve, x = -5, x = 5 and the x axis is:''')
   lowerCAmelCase__              =							10
   while i <= 100000:
      print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
      i *= 10










"""simple docstring"""


import itertools
import math


def        UpperCAmelCase      (					a__ ):





						'''simple docstring'''






						if 1 < number < 4:
												# 2 and 3 are primes
												return True
						elif number < 2 or number % 2 == 0 or number % 3 == 0:
												# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
												return False

						# All primes number are in format of 6k +/- 1
						for i in range(5     ,      int(math.sqrt(a__ ) + 1 )     ,      6 ):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True


def        UpperCAmelCase      (					):





						'''simple docstring'''






						lowerCAmelCase   :str						=			2
						while True:
												if is_prime(a__ ):
																		yield num
												num += 1


def        UpperCAmelCase      (					a__ = 1_00_01 ):





						'''simple docstring'''






						return next(itertools.islice(prime_generator()     ,      nth - 1     ,      a__ ) )


if __name__ == "__main__":
		print(F"""{solution() = }""")